Some remarks on the existence of compact multiply Einstein warped products

The aim of this paper is to study the existence of compact multiply Einstein warped products M=Bxf1F1xf2F2x<middle dot><middle dot><middle dot>xfnFn,fi:B ->(0,infinity),fi is an element of C infinity(B) for everyi is an element of{1,...,n},n >= 1. We prove the following:(a)lambda>0where lambda is the Einstein constant of M,(b)mu i>0where mu iis the Einstein constant of Fi for every i is an element of {1,...,n},(c) dimB >= 2 and dim Fi >= 2 for every i is an element of {1,...,n},(d) dimB >= 3 for equal warping functions.